## Extra Credit 5

### Ramp: Forces and motion

Use an on-line simulation from the University of Colorado PhET group to explore the behavior of objects that are just placed on, or pushed up and down a ramp.

A free body diagram of an object on a frictionless ramp is shown above.   The y-component of the weight mg of the object is exactly canceled by the normal force of magnitude N.  The x-component of the weight accelerates the object down the ramp.

On a real ramp the object and the ramp will interact via the frictional force.  The coefficients of static friction, μs, and kinetic friction, μk, which depend on the type of surfaces that are in contact with each other, are used to calculate the maximum force of static friction and the force of kinetic friction.

fs ≤ μsN,  fk = μkN.

The frictional force always points in a direction to oppose the relative motion of the surfaces.
For the interaction between the object and the ramp fs_max = μsmg cosθ,  fk = μkmg cosθ.

Procedure:

Open the" Ramp:  Forces and Motion" simulation.

Explore the interface!

• Try the different tabs at the top of the simulation.  Concentrate on the first three tabs.
• Explore the options in the panel on the right side of the simulation.